The bicycle gear-shifting mechanism is generally composed of two sprocket sets and a sprocket chain fastening the two sprocket sets for transferring motion from one sprocket set to another. The sprocket sets are provided respectively with a cluster of gears having teeth of various sizes. The speed-changing process of bicycle is attained by an action of pulling the transmission cable so as to actuate the sprocket chain to move from one sprocket gear to another.
The smooth operation of such a bicycle gear-shifting mechanism as described above depends on the curved angle and the sideway deflection of the chain links of the sprocket chain. For this reason, the U.S. Pat. No. 4,889,521 discloses a bicycle sprocket assembly, which is constructed on the basis of a theory that the path, on which the sprocket chain is moved from the small sprocket gear to the large sprocket gear, is corresponding to a line tangent to the line formed between the gear pitch center of the small sprocket gear and the gear pitch center of the large sprocket gear. The interval L of the tangent paths is integral to the lengths of the sprocket chain link pieces. On the other hand, the U.S. Pat. No. 5,162,022 discloses a bicycle sprocket assembly, which is constructed on the basis of a theory that the interval L of the tangent paths of the sprocket chain is not integral to the lengths of the sprocket chain link pieces, and that the sprocket chain is engaged with the grooves of the large sprocket gear in a progressively slow pace.
The prior art disclosures referred to above place the emphasis on the first half of the gear-shifting process without regard to the second half of the gear-shifting process, in which the curved angle and the sideway deflection of the sprocket chain are important elements that must be taken into consideration so as to avert the incident of the mechanical interference of the sprocket gear by the sprocket chain.